Characterization of Dielectric Properties of Graphene and Graphite Using the Resonant Cavity in 5G Test Band

Abstract

This paper presents a study about the dielectric constant ε_r, dielectric loss tangent tan g(δ) and effective electrical conductivity σ_e of graphene, graphite and graphene-bakelite combination using the resonant cavity method. For this purpose, cylindrical samples with diameter of 30 mm and thickness of 4.5 mm were analyzed taking into account the central frequency f₀ = 3.5 GHz, according to 5G technology standards. The constants ε_r and tan g(δ) were obtained from the resonance frequency f_a of measured scattering parameters (S-parameters), when the cavity was loaded with the samples. An empirical equation was developed to model the relation between f_a and ε_r. With this empirical equation it was found ε_r = 9.3203 and tan g(δ) = 0.7000 for graphene and ε_r = 17.1508 and tan g(δ) = 0.2700 for graphite. The addition of bakelite in combination with graphene allowed controlling the dielectric properties of these composites. The results, obtained in this macroscale characterization, are interesting for Telecommunications Engineering, especially in the development of radiation-absorbent material, which is suitable for mitigation of interference between different wireless communication systems.

Index Terms
Dielectric constant; dielectric loss constant; resonant cavity; graphene; graphite

I. Introduction

The investigation of dielectric properties of materials is particularly interesting for Telecommunications Engineering, especially in Microwave Engineering, Antenna Theory and industry of devices for communication systems. Among these properties, the relative electrical permittivity (ε_r) and the dielectric loss tangent (tan g(δ)) can be considered the most relevant ones [¹], [²]. In the last years, graphene has become the most interesting carbon allotrope for the development of new materials, because of its promising possibilities in terms of technological applications [³]. In this context, the investigation of the dielectric properties of graphene and graphite is relevant, since it supports new potential applications.

In terms of molecular arrangement, graphene is formed by long two-dimensional chains whose unit cells have hexagonal geometry, derived from connections of carbon atoms, ideally of the sp²-type. A specific configuration case of this system is the micro-structural configuration of graphite, in which the two-dimensional chains are superimpose forming a three-dimensional structure [²]-[⁴].

Considering microscale analysis, graphene exhibits excellent electrical conduction capability. For this reason, graphene films (with thicknesses of the order of nanometers) can be used as electrically conductive structures in the design of nano-antennas for communications in the higher bands (higher than 10 GHz) of the 5^th generation of mobile communication systems (5G). Sa'don et al. presented a study about the design of a single element and an array of graphene printed antennas, in coplanar-waveguide (CPW) technology for operation frequency at 15 GHz [⁵]. This structure consists in a graphene layer with thickness of 100 nm, printed on a Kapton film substrate with thickness of 76 μm. The authors reported gain values of 2.87 dBi and 9.28 dBi for the single element and the array antennas, respectively.

On the other hand, taking into account macroscale analysis, graphene can be also used as “inserted component” in radiation-absorbent material (RAM). Tantis et al. showed the insertion of two-dimensional graphene structures into polymeric matrices - poly(vinyl alcohol) nanocomposites [⁶]. Four different concentrations of graphene oxide were considered (1-3 wt% and 5 wt%). The authors observed that the variation of graphene oxide inserted into the matrix controls its dielectric constant and dielectric loss tangent values. Bispo et al. described a study about the different polymeric composites production based on polystyrene matrix [⁷]. The composites produced with xerogel, carbon-graphene and graphite presented the most efficient results in terms of electromagnetic absorption in X-band (8.2 – 12.4 GHz), where about 87% of the incident electromagnetic power was absorbed by these samples. These analyses were performed considering the macroscale effects of graphene interacting with electromagnetic fields.

The use of resonant cavities is a classic approach for the determination of the properties ε_r and tan g(δ) of dielectric materials. This device is typically hollow, with metallic walls composing a cylindrical or a rectangular shape. When a dielectric sample with ε_r > 1 is inserted into the cavity, its resonance frequency f₀ decreases, due to perturbation of the internal electromagnetic field. From this frequency shift, the ε_r constant of the sample can be derived [⁸]-[¹⁰]. The reports by Rubinger and Costa [¹¹] and Zhang et al. [¹²] used the resonant cavity method for characterization of dielectric constants of polymeric samples. These parameters were mathematically obtained with specific equations, proposed by the authors, so as to link the measured frequency (for each sample) to the ε_r constant. In general, up to now, there are several studies about the dielectric properties characterization of graphene and graphite at different frequencies [¹³]-[¹⁵], but not at 3.5 GHz using the resonant cavity method.

Therefore, taking into account the previous comments, in this work, an experimental study for the macroscale characterization of dielectric and loss tangent constants of graphite, graphene and graphene-bakelite combinations using a cylindrical resonant cavity is presented. Initially, the technical details of the design and fabrication of the cavity are presented. Then, a mathematical modeling of this experimental setup is derived and empirical equations for ε_r and tan g(δ) assessments are proposed. This approach is validated by the characterization of samples in macroscale, whereby graphene and graphite demonstrated to have large loss constants in the 5G test frequency 3.5 GHz. This feature indicates that both are potential candidates to be used in the development and production of new radiation-absorbent materials (RAMs). This property is very interesting to mitigate inference between different wireless communication systems.

The next section presents the methodology used in this study. In section 3, the procedure for preparation of the samples and the used materials are described. The measured data (in terms of resonance frequency for each sample) and estimations for ε_r, tan g(δ) and σ are presented and discussed in section 4. Finally, the conclusions of this work are drawn.

II. Design of the experimental setup

A. Design of the resonant cavity

The design frequency (f₀) was defined as 3.5 GHz, because this is the testing frequency for the development of new technologies for the 5G systems [¹⁶] [¹⁷]. Next, the cavity geometry has been defined to be cylindrical, due to fabrication issues. The cavity dimensions have been optimized using the electromagnetic simulator ANSYS HFSS^® software and are summarized in Table 1, where a is the inner radius, d is the inner height and l is the length of the excitation elements (copper wires).

Table I
Physical Dimensions of the cylindrical resonant cavity

Dimension	Optimized Value (mm)
a	32. 40
d	41. 50
l	7. 56

The prototype of this resonant cavity was divided in two parts: the hollow main body and the cover. The excitation elements have been attached to the latter. Both parts were produced with aluminum, with the dimensions a and d as listed in Table I, and are shown in Fig. 1 (a) an (b). The excitation elements, which consist of two female SMA connectors with inner conductors extended with copper wires coated with nylon polymer, are shown in Fig. 1 (c).

Fig. 1
Parts of the cylindrical resonant cavity prototype: (a) Hollow main body; (b) Cover and (c) Excitation elements.

A vector network analyzer (VNA) model E5071C (Agilent Technologies) was used for the measurements of the S-parameters for the resonant cavity loaded with graphene, graphite and graphene-bakelite samples. The resonance frequency of the loaded cavity f_a can be obtained with this setup and is determined by assessing the frequency for which the lowest value of S₁₁ is verified. The dielectric constants, of each sample can be estimated from f_a with an empirical mathematical equation formulated for ε_r, whereas the loss tangent can be assessed by parametric simulations with ANSYS HFSS^®. The tan g(δ) parameter is varied in the simulation model, and its experimental value can be inferred since that, the simulated value of S₂₁ approaches the magnitude of the measured S₂₁ in the pass-band.

B. Mathematical Modeling for the ε_r and tan g(δ)calculation

The dielectric constant of the samples is calculated from f_a, obtained from the measured S₁₁-parameter, when the sample is placed inside the resonant cavity. For the ε_r calculation, a parametric study was performed in ANSYS HFSS^® software, by varying ε_r from 2 to 20, with a step of 1, in order to assess the resulting f_a values and to allow estimating the most appropriate equation for the modeling of the proposed experimental setup.

The mathematical representation is based on the literature for the generalized equations for modeling the perturbation in the resonant cavity [¹⁸] and experimental studies presented by Rubinger and Costa [¹¹] and Costa et al. [¹⁹]. In these papers, the authors show that ε_r is related to (f₀ – f_a)/f₀ ratio through an empirical equation, which holds exclusively for a given setup (in terms of geometry and dimensions of the cavity and of the samples). The general representation of this relation is given by [¹⁸].

(1) $$(f_0-f_a)/f_0=F({\epsilon }_r-1)$$

From the most suitable function F(x) (with x = ε_r – 1) that describes the relation between ε_r and f_a, the argument x can be isolated and estimated according to the measured f_a for each characterized sample. Finally, considering ε_r = x + 1, the dielectric constant for each sample can be calculated.

From the generalized representation given by Eq. (1), the mathematical modeling of the present study is developed. In the present study, the samples exhibit cylindrical shape with diameter of 30 mm and thickness of 4.5 mm. The obtained data in parametric analysis with ANSYS HFSS^® simulator are listed in Table II. In Fig. 2, the graphical representation of this “calibration curve” for (f₀ – f_a)/f₀ as a function of ε_r – 1 is presented.

Table II
Values Of F_a (GHz) obtained with the parametric analyses with ansys hfss^®

εr	εr – 1	fa (GHz)	(f0 – fa)/f0
2	1	3.4350	0.0157
3	2	3.4070	0.0238
4	3	3.3930	0.0278
5	4	3.3820	0.0309
6	5	3.3740	0.0332
7	6	3.3670	0.0352
8	7	3.3600	0.0372
9	8	3.3560	0.0384
10	9	3.3520	0.0395
11	10	3.3510	0.0398
12	11	3.3450	0.0415
13	12	3.3410	0.0427
14	13	3.3400	0.0430
15	14	3.3350	0.0444
16	15	3.3330	0.0450
17	16	3.3300	0.0458
18	17	3.3260	0.0470
19	18	3.3250	0.0473
20	19	3.3190	0.0490

Fig. 2
Calibration curve for the experimental setup designed in this work.

The mathematical representation that adequately describes the calibration curve in Fig. 2 is given by:

(2) $$(f_0-f_a)/f_0=0.0108\ln ({\epsilon }_r-1)+0.0158$$

Isolating the term ε_r, the final form of the mathematical representation for this experimental setup is given by

(3) $${\epsilon }_r=e^{\left[\frac{(f_0-f_a)/f_0-0.0158}{0.0108}\right]}+1$$

These equations are valid only for the mathematical modeling for the proposed setup and for the 5G test frequency 3.5 GHz. For other cases, e.g. other frequency of interest, a new calibration curve must be obtained using the methodology explained here.

C. Calculation of Effective Electrical Conductivity

The general mathematical representation of tan g(δ) relates to electrical conductivity as

(4) $$\tan g(\delta )=\frac{{\sigma }_0+\omega {\epsilon }^{\prime \prime }}{\omega {\epsilon }^{\prime }}$$

Where, σ₀ denotes the static electrical conductivity (S/m), ω = 2πf_a is the angular frequency, in rad/s, ε′ and ε″ are the real and imaginary components of the electrical permittivity, given in F/m [²⁰].

The term ωε″ can be also identified as the component of effective electrical conductivity (σ_e) due to the imaginary part of the electrical permittivity. Thereby,

$${\sigma }_{\alpha }=\omega {\epsilon }^{″}$$

(5) $${\sigma }_e={\sigma }_0+{\sigma }_{\alpha }$$

Finally, replacing (5) in (4), we can obtain

(6) $$\tan g(\delta )=\frac{{\sigma }_e}{\omega {\epsilon }^{\prime }}$$

With this equation, one can estimate the effective electrical conductivity from the calculated tan g(δ) for each sample [²⁰].

D. Samples Specifications

The commercial graphene and graphite used in this work were provided by the Brazilian companies Amazonas Grafeno and Nacional Grafite, respectively. Fig. 3 shows an image MEV (a), where it is possible to see the graphene layers, and an average Raman spectrum (∼ 14 spectra taken at different places of one sample) (b) with its characteristic Raman bands (D, G, 2D e 2D^’), of the graphene powder used to prepare the samples. For these measurements the powder was placed on a SiO₂ substrate using the micromechanical method. In order to verify the number of graphene layers the integrated intensity ratio I_2D/I_G was calculated, finding the value of ∼ 0.6. It is well known that, for free-defect graphene, the I_2D/I_G is dependent on the number of graphene layers [²¹]. The ratio I_2D/I_G ∼ 2–3.5 is for monolayer graphene, 1 < I_2D/I_G <2 for bilayer graphene and I_2D/I_G < 1 for few layers graphene (FL) as shonw on Fig. 3(a). The samples were produced using the embedding process.

Fig. 3
(a) Image MEV and (b) average Raman spectrum of few layers of commercial graphene (Amazonas).

Fig. 4 shows samples of graphene (gn100) (a) and graphite (gt100) (b) produced from powdered materials (5.5251 g for graphene, and 5.8939 g for graphite), which were singly entered in a hydraulic piston at a constant pressure of 1000 lb/inch² and by applying a heating ramp from 25 °C to 145 °C during 7 minutes. The top temperature (145 °C) was then kept during additional 8 minutes. The final result is a pastille formed by the aggregation of powdered particles.

Fig. 4
Produced graphene and graphite samples: (a) gn100 and (b) gt100 and Bakelite-graphene produced samples (c) gn40; (d) gn50 and (e) gn60.

The zoomed pictures of the samples gn100 and gt100 (shown in Fig. 4(a) and (b)) are homogeneous and uniform, with some clusters of the material (white dots), indicating that the embedding process was effective in compacting the powder materials.

Samples based on the mixture of three different combinations of graphene and bakelite (powdered polymer that becomes solid) with the procedure described above were also produced for the verification of dielectric properties. The concentration (in %) of graphene and bakelite and their respective masses (g) are shown in Table III.

Table III
Composition of the bakelite-graphene samples

Proportion: Bakelite-graphene	bakelite (g)	graphene (g)
100% - 0% (bk100)	5.5534	0.0000
60% - 40% (gn40)	3.3322	2.3490
50% - 50% (gn50)	2.7767	2.9398
40% - 60% (gn60)	2.2214	3.5262

The resulting bakelite-graphene samples are shown in Figs. 4 (c) – (e). The addition of bakelite in these mixtures results in the hardest samples to handle and are more suitable for experimental characterization. As seen for the samples gn100 and gt100 (Fig. 4 (a) and (b)), the zoomed pictures of the samples gn40, gn50 and gn60 (shown Fig. 4 (c - e)), taken with a x10 objective lens of an optical microscope, are also homogeneous and uniform to investigate the dielectric properties at the frequency of 3.5 GHz. It is worth to emphasize that, this frequency can be still considered as low frequency, and then the sample surface does not show significant irregularities that compromise the results at this frequency.

III. Experimental Results

The samples described in the previous section were inserted, one at a time, into the resonant cavity and the S-parameters were measured. Fig. 5 shows a comparison of the S₁₁ (a) and S₂₁ (b) parameters for gn100 and gt100 samples with the measured parameters considering the unloaded cavity (UC, blue curves of S₁₁ and S₂₁). In both cases, the minimum values of S₁₁ and maximum of S₂₁. The results obtained are plotted in Fig. 5 for samples gn100 and gt100. These measured values for the graphite sample exhibit larger shifts to lower frequencies when compared to the graphene sample. This behavior indicates that the dielectric constant of graphite is higher than that of graphene. According to Fig. 5 (a), the resonance frequency of the cavity loaded with the sample gn100 is f_a = 3.3550 GHz and, for gt100, it is f_a = 3.3300 GHz. Using these values, the estimated dielectric constants are ε_r = 9.3203 for graphene and ε_r = 17.1508 for graphite.

Fig. 5
Measured (a) S₁₁-parameters and (b) S₂₁ parameters for samples gn100 and gt100.

As mentioned before, most studies about the dielectric properties characterization of graphene, reported in the literature, consider the analysis of nanometric structures and its results are very divergent from each other. In a different way, the present work considers the dielectric properties characterization of graphene in macroscale. For instance, Bessler et al. [²²] characterized the resulting dielectric constant of a bilayer graphene (BLG) with the atomic force microscopy (AFM) technique. Their analyzed the effects of the microscopic structure of the material and the interactions between the two graphene layers, reporting a dielectric constant of ε_r = 6.0000, for BLG. However, Cismaru et al. [²³] obtained a different experimental result using a different characterization method. In their study, a single layer graphene (SLG) was deposited on a gold substrate to compose a coplanar waveguide (CPW) structure. Their samples were characterized from 5 to 40 GHz, obtaining ε_r ≈ 16.00 at the frequency of 5 GHz. The difference between our results with those reported by other authors is attributed to the use of different characterization techniques applied at different frequencies. The cited studies developed graphene characterization in microscale, while this work considers the characterization of graphene in macroscale and at a lower frequency than the reported by the authors. According to this, we can argue that different characterization methods and frequencies of analysis will give different responses of the dielectric properties.

For instance, Hotta et al. [²⁴] has presented the characterization of dielectric properties of carbonaceous materials, considering frequencies from 1 GHz to 10 GHz, using the rectangular section waveguide method. In this study, the measured ε_r constant for the graphite sample is equal to 17.00 in the frequency of 3.5 GHz. Additionally, the authors report that the ε_r constant of graphite change as the frequency characterization changes. Therefore, we can infer that the characterization methodology adopted in this work is able to provide reliable estimation for ε_r.

As shown in Fig 5 (b), the peak magnitude of the measured S₂₁-parameter in f_a = 3.3550 GHz for the gn100 sample is −5.8510 dB. For gt100 sample, it is −3.4430 dB at f_a = 3.3300 GHz. The peak magnitude of the measured S₂₁-parameter for the unloaded cavity is −0.8210 dB. This reduction in the peak magnitude for the loaded cavity demonstrates the influence of the tan g(δ) constant on the analyzed materials. For the determination of dielectric loss tangents of the samples, some parametric simulations in ANSYS HFSS^® software, considering the calculated ε_r constant for each sample, were performed. The correct value of tan g(δ) is the one where the simulated S₂₁-parameter curve approaches the corresponding measured S₂₁-parameter curve.

According to this procedure, the gn100 sample has tan g(δ) = 0.7000 and the gt100 sample has tan g(δ) = 0.2700. These dielectric loss tangent values are very high and the characterized materials can be considered as very good electromagnetic absorbers at the frequency of interest. These materials have the capability to dissipate energy in its structure, hence producing large attenuation of the electromagnetic waves. For instance, for the gn100 sample, 68.45% of the power coupled to the cavity is dissipated by the sample, and, for gt100, this reduces to 45.32%. Hotta et al. [²⁴] verified that tan g(δ) ≈ 0.5294 for graphite. This difference can be explained because the authors did not directly characterized this property, but estimated with theoretical equations.

Fig. 6 (a) and (b) show the S₁₁ and S₂₁-parameters for samples manufactured by bakelite-graphene combinations. Measured S₁₁-parameters for the loaded cavity with 40% graphene and 50% graphene samples (gn40 and gn50) resulted in f_a values very close to each other, resulting in ε_r values slightly different, as shown in Table IV. However, the sample gn60 (with 60% graphene) presented the same result obtained with sample gn100, i.e. f_a = 3.3550 GHz and ε_r = 9.3203. Table 4 shows the ε_r constants calculated for these analyzed samples along with the obtained tan g(δ) constant in the parametric simulations in ANSYS HFSS^® software.

Fig. 6
Measured (a) S₁₁-parameters and (b) S₂₁-parameters for bakelite-graphene combinations samples.

Table IV
Dielectric properties of the bakelite-graphene characterized samples

sample	fa(GHz)	εr	Measured S21f (dB)	Simulated S21f (dB)	tan g(δ)
UC	–	–	-0.8210	-0.1101	-
bk-100	3.3750	5.8940	-1.8390	-1.1280	0.0840
gn40	3.3585	8.5825	-2.7010	-1.9902	0.1410
gn50	3.3565	8.9957	-2.9800	-2.2692	0.1720
gn60	3.3550	9.3203	-3.3330	-2.6223	0.2480

According to the results presented in Fig. 6 (a) and (b) and the numerical results listed in Table IV, different bakelite-graphene combinations yield different electromagnetic absorption capacity in comparison to the experimental response for sample gn100 (see Fig. 7 (a) and (b)). The dielectric-loss constant of bakelite (sample bk100) is lower than that one of graphene. The characterization of the reference sample resulted in f_a = 3.3750 GHz, ε_r = 5.8940 and tan g(δ) = 0.0840. Therefore, the combination of two materials with different characteristics results in a composite with properties that can be controlled based on their concentrations: higher graphene concentrations result in composites with higher tan g(δ) and ε_r values, whereas higher bakelite concentrations result in composites with lower tan g(δ) and ε_r constants.

Fig. 7
Effect of different bakelite concentration on (a) dielectric constant and (b) dielectric loss tangent.

These experimental data demonstrate the linear relation (region between dashed red lines) existing between ε_r and the bakelite concentration (in %). The variation of ε_r and tan g(δ) is inversely proportional to the bakelite concentration, as shown in Fig. 7(a) and (b). Therefore, the parameters ε_r and tan g(δ) on the graphene composites tend to decrease accordingly as the concentration of a material with lower constants ε_r and tan g(δ) increases.

The effect of increasing ε_r constant with the addition of higher concentrations of graphene in the samples was also reported by others authors, considering different frequencies of analysis and matrix materials, but their results indicates the same deportment related in the present work. For instance, Bispo et al. [⁷] produced and characterized the dielectric properties of samples based in a polymeric matrix (polystyrene) with insertion of 10% of Carbon-Graphene Xerogel (CGX). The resulting measured dielectric constant (considering X-band, 8.2 – 12.4 GHz) was ε_r (CGX) = 4.00. However, the reference sample (100% polystyrene) had a dielectric constant ε_r (matrix) = 2.99. And, Liu et al. [²³] also verified that the insertion of different concentrations of graphene oxide in a polyimide matrix resulted in different ε_r constants. For the highest concentration of graphene oxide (1%) the measured dielectric constant was 8.00 and the dielectric constant of the reference sample (100% polyimide resin) was ε_r (matrix) = 3.50. These experimental results were obtained at 1 MHz.

The increase of tan g(δ) for higher concentrations of graphene in the samples was also observed by Liu et al. [²⁵] even though considering different conditions of frequencies of analysis and matrix material. The authors verified that the insertion of different concentrations of graphene oxide in a polyimide resin matrix resulted in samples with different dielectric-loss constants. For the highest concentration of graphene oxide (1%) the measured tan g(δ) was 0.12 with tan g(δ) (matrix)= 0.02 for the reference sample (100% polyimide resin). These experimental parameters were also obtained at 1 MHz.

According to these experimental results, it is convenient to state that the insertion of controlled concentrations of graphene into a specified matrix causes the increase of their dielectric properties ε_r and tan g(δ). It is worth also to emphasize that different authors have determined the dielectric properties of graphene oxide mixing them with different materials and at different frequencies, but as mentioned in the introduction section so far there are not studies of these properties on graphene in the 5G test band (3.5 GHz). These results can contribute for making use these dielectric properties for the development of new RAMs.

Finally, in Table V the estimated values of electrical conductivity, obtained with Eq. (6), for samples gt100, gn100, gn60, gn50 and gn40, are presented. The high values of σ_e, obtained for the samples gt100 (σ_e = 856.7000 S/mm) and gn100 (σ_e = 1216.0000 S/mm) reinforce the optimal quality of effective electrical conductivity of graphene and graphite.

Table V
Calculated values of electrical conductivity of samples from graphite, graphene and graphene-bakelite combinations

sample	tan g(δ)	σe (S/mm)
gt100	0.2700	856.7000
gn100	0.7000	1216.0000
gn60	0.1410	430.8000
gn50	0.1720	288.5000
gn40	0.2480	225.8000

Mohan et al. [²⁶] reported the experimental characterization of the electrical conductivity of graphene oxide. The authors obtained the maximum value of σ_e = 100.0000 S/mm for analyzed samples. On other hand, Marinho et al. [²⁷] described that the electrical conductivity of compact graphene structures present values varying to the pressure applied in the samples. For minimal values of pressure (approximate to 0 MPa), the authors verified that σ_e ≈ 100.0000 S/mm for graphene sample.

Marinho et al. [²⁷] also reported that the σ_e constant of compact graphite structures present values varying to the pressure applied in the samples. In this analysis, the authors showed that, for minimal values of pressure applied in the compression of the samples, the resultant estimated electrical conductivity of sample based in graphite with density equal to 0.8600 g/cm³ is σ_e ≈ 900.0000 S/mm. This specific result is comparable to the obtained in the present work for gt100 sample.

In addition, the mixture of bakelite with graphene causes a great reduction in σ_e. This fact can be explained because bakelite has tan g(δ) lower than graphene and, consequently, its electrical conductivity is also smaller. Then, its combination with graphene yields a composite with reduced electrical conducting capacity.

V. Conclusion

In this work, we reported the characterization of dielectric properties of graphene, graphite and different combinations of bakelite-graphene, considering the test band of 5G (3.5 GHz), and compared these obtained data with previous works found in the literature. Samples entirely produced from graphene and graphite, and samples produced from three different combinations of graphene and bakelite, were analyzed. The high experimental values obtained suggest that these carbonaceous materials are very interesting for the development of technologies for electromagnetic radiation absorbing materials in the radiofrequency spectrum. It was demonstrated in the analysis of bakelite-graphene samples that it is possible to control the dielectric properties of the composites according to the adequate choice of the proportional concentrations of graphene and the matrix material (bakelite, in this work) in the same way as described in the literature. This is very interesting for different applications such as Stealth devices and absorbers materials for anechoic chambers. In addition, the optimal characteristic of electrical conductivity for graphene and graphite also was verified by means of the estimates for σ_e constant from the tan g(δ) data. These values are in agreement with other studies previously reported in the literature.

Acknowledgments

The authors would like to thank to Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES for the fellowship to V. M. Pereira; to CNPq for the fellowship to Luis E. G. Armas; and the Federal University of Pampa – UNIPAMPA for Experimental facilities.

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Publication Dates

• Publication in this collection
  13 Mar 2023
• Date of issue
  Mar 2023

History

• Received
  02 June 2022
• Reviewed
  15 June 2022
• Accepted
  19 Dec 2022